Thibault Lemaire

Study of the Influence of Fibrous Pericellular Matrix in the Cortical Interstitial Fluid Movement With Hydroelectrochemical Effects

Fluid flow within cortical bone tissue is modeled through an upscaling approach of a local description of the fluid movement. At the pore scale, the coupled phenomena (Poiseuille effect, osmosis, and electro-osmosis) governing the interstitial fluid movement are considered. Thus, actions of electro-osmotic and osmotic motions, in addition to the classical Poiseuille flow, are studied at the canaliculus scale by deriving a coupled Darcy law. The addition of a Brinkman-like term in this macroscopic result helps us to take into account the influence of the pericellular matrix on the coupled transport phenomena. At the canaliculus scale, the general trends that can be drawn from this study are as follows: (i) The presence of the fibrous matrix tends to reduce the fluid flow considerably; (ii) the role of osmotic and electro-osmotic effects is no longer negligible for dense fibrous media.

Periosteum, bone's “smart” bounding membrane, exhibits direction‐dependent permeability

The periosteum serves as bones bounding membrane, exhibits hallmarks of semipermeable epithelial barrier membranes, and contains mechanically sensitive progenitor cells capable of generating bone. The current paucity of data regarding the periosteums permeability and bidirectional transport properties provided the impetus for the current study. In ovine femur and tibia samples, the periosteums hydraulic permeability coefficient, k, was calculated using Darcys Law and a custom‐designed permeability tester to apply controlled, volumetric flow of phosphate‐buffered saline through periosteum samples. Based on these data, ovine periosteum demonstrates mechanically responsive and directionally dependent (anisotropic) permeability properties. At baseline flow rates comparable to interstitial fluid flow (0.5 µL/s), permeability is low and does not exhibit anisotropy. In contrast, at high flow rates comparable to those prevailing during traumatic injury, femoral periosteum exhibits an order of magnitude higher permeability compared to baseline flow rates. In addition, at high flow rates permeability exhibits significant directional dependence, with permeability higher in the bone to muscle direction than vice versa. Furthermore, compared to periosteum in which the intrinsic tension (pre‐stress) is maintained, free relaxation of the tibial periosteum after resection significantly increases its permeability in both flow directions. Hence, the structure and mechanical stress state of periosteum influences its role as bones bounding membrane. During periods of homeostasis, periosteum may serve as a barrier membrane on the outer surface of bone, allowing for equal albeit low quiescent molecular communication between tissue compartments including bone and muscle. In contrast, increases in pressure and baseline flow rates within the periosteum resulting from injury, trauma, and/or disease may result in a significant increase in periosteum permeability and consequently in increased molecular communication between tissue compartments. Elucidation of the periosteums permeability properties is key to understanding periosteal mechanobiology in bone health and healing, as well as to elucidate periosteum structure and function as a smart biomaterial that allows bidirectional and mechanically responsive fluid transport.

What is the importance of multiphysical phenomena in bone remodelling signals expression? A multiscale perspective.

Cortical bone, constituting the outer shell of long bones, is continuously renewed by bone cells in response to daily stimuli. This process, known as bone remodelling, is essential for proper bone functioning in both physiological and pathological conditions. Classical bone remodelling models do not, or only implicitly do, take into account physico-chemical phenomena, focussing on the mechanosensitivity property of the tissue. The aim of this paper is to carry out an investigation of the multiphysical phenomena occuring in bone life. Using a recent multiscale model combining piezoelectricity and electrokinetics to poromechanics, the usual viewpoint of bone remodelling models is questioned and new research avenues are proposed.

A multiscale theoretical investigation of electric measurements in living bone : piezoelectricity and electrokinetics.

This paper presents a theoretical investigation of the multiphysical phenomena that govern cortical bone behaviour. Taking into account the piezoelectricity of the collagen–apatite matrix and the electrokinetics governing the interstitial fluid movement, we adopt a multiscale approach to derive a coupled poroelastic model of cortical tissue. Following how the phenomena propagate from the microscale to the tissue scale, we are able to determine the nature of macroscopically observed electric phenomena in bone.

Multiphysical modelling of fluid transport through osteo-articular media

In this study, a multiphysical description of fluid transport through osteo-articular porous media is presented. Adapted from the model of Moyne and Murad, which is intended to describe clayey materials behaviour, this multiscale modelling allows for the derivation of the macroscopic response of the tissue from microscopical information. First the model is described. At the pore scale, electrohydrodynamics equations governing the electrolyte movement are coupled with local electrostatics (Gauss-Poisson equation), and ionic transport equations. Using a change of variables and an asymptotic expansion method, the macroscopic description is carried out. Results of this model are used to show the importance of couplings effects on the mechanotransduction of compact bone remodelling.

On the paradoxical determinations of the lacuno-canalicular permeability of bone

The lacuno-canalicular permeability has been shown to play a key role in the behavior of bone tissue. The aim of this study is, by giving an overview of the determinations of this parameter, to question the paradoxical values provided by theoretical predictions and recent experimental measurements. We propose therefore a Kozeny-like law obtained by a numerical method which relates the permeability to the textural parameters of cortical bone microstructure. Moreover, we suggest possible explanations for this paradox considering the empirical difficulties and possible multiphysical effects.

Poroelastic behaviour of cortical bone under harmonic axial loading: A finite element study at the osteonal scale

Bone fluid flow and its induced effects on the bone cells are important players in triggering and signalling bone formation and bone remodelling. This study aims to numerically investigate the behaviour of interstitial fluid flows in cortical bone under axial cyclic harmonic loads that mimics in vivo bone behaviour during daily activities like walking. Here, bone tissue is modelled as a fluid-saturated anisotropic poroelastic medium which consists of a periodic group of osteons. By using a frequency-domain finite element analysis, the fluid velocity field is quantified for various loading conditions and bone matrix parameters.

Interstitial fluid flow within bone canaliculi and electro-chemo-mechanical features of the canalicular milieu: a multi-parametric sensitivity analysis.

Canalicular fluid flow is acknowledged to play a major role in bone functioning, allowing bone cells’ metabolism and activity and providing an efficient way for cell-to-cell communication. Bone canaliculi are small canals running through the bone solid matrix, hosting osteocyte’s dendrites, and saturated by an interstitial fluid rich in ions. Because of the small size of these canals (few hundred nanometers in diameter), fluid flow is coupled with electrochemical phenomena. In our previous works, we developed a multi-scale model accounting for coupled hydraulic and chemical transport in the canalicular network. Unfortunately, most of the physical and geometrical information required by the model is hardly accessible by nowadays experimental techniques. The goal of this study was to numerically assess the influence of the physical and material parameters involved in the canalicular fluid flow. The focus was set on the electro-chemo-mechanical features of the canalicular milieu, hopefully covering any in vivo scenario. Two main results were obtained. First, the most relevant parameters affecting the canalicular fluid flow were identified and their effects quantified. Second, these findings were given a larger scope to cover also scenarios not considered in this study. Therefore, this study gives insight into the potential interactions between electrochemistry and mechanics in bone and provides the rational for further theoretical and experimental investigations.

Influence of interstitial bone microcracks on strain-induced fluid flow.

It is well known that microcracks act as a stimulus for bone remodelling, initiating resorption by osteoclasts and new bone formation by osteoblasts. Moreover, microcracks are likely to alter the fluid flow and convective transport through the bone tissue. This paper proposes a quantitative evaluation of the strain-induced interstitial fluid velocities developing in osteons in presence of a microcrack in the interstitial bone tissue. Based on Biot theory in the low-frequency range, a poroelastic model is carried out to study the hydro-mechanical behaviour of cracked osteonal tissue. The finite element results show that the presence of a microcrack in the interstitial osteonal tissue may drastically reduce the fluid velocity inside the neighbouring osteons. This fluid inactive zone inside osteons can cover up to 10% of their surface. Consequently, the fluid environment of bone mechano-sensitive cells is locally modified.

Do calcium fluxes within cortical bone affect osteocyte mechanosensitivity

Bone reacts to local mechanical environment by adapting its structure. Bone is also a key source of calcium for the body homeostasis. Osteocytes, cells located within the bone tissue, are thought to play a major role in sensing mechanical signals and regulating bone remodeling. Interestingly, osteocytes were also shown to directly participate in the calcium homeostasis by regulating dissolution and deposition of calcium in the perilacuno-pericanalicular space. However, it is not known if osteocytes roles in mechanoregulation and calcium homeostasis have any significant crosstalk. Previously, a multi-scale mathematical model of the interstitial fluid flow through the canaliculus was developed, which took into account physicochemical phenomena including hydraulic effects, formation of electrical double layer, osmosis and electro-osmosis. We extended this model to include the directional movement of calcium from and into the bone tissue, and assessed the shear stress at the osteocyte membrane. We have found that in the bulk of the canalicular space the fluid flow due to chemical gradient generated by deposition or dissolution of calcium is negligible compared to the fluid flow due to hydraulic pressure. However, at the osteocyte proximity, the presence of calcium gradient generated sufficient fluid flow to induce significant changes in the shear stress on the osteocyte membrane. Calcium deposition and dissolution on the canalicular wall resulted in increased or decreased shear stress on the osteocyte membrane respectively. Thus, our data demonstrate that strong calcium fluxes due to whole body calcium homeostasis may affect mechanical forces experienced by osteocytes.